Questions tagged [thermodynamics]

Covers the study of (mostly homogeneous) macroscopic systems from a heat/energy/entropy point of view. Consider also using tag: [statistical-mechanics].

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Legendre transform of $S(E,V)$ to obtain $F(T,V)$

So, using the legendre transform: $$g=f-x\left ( \frac{df}{dx} \right )_y$$ I tried to obtain the Helmholtz free energy from Entropy and I got: $$F(T,V)=S(E,V)-E\left ( \frac{\partial S}{\partial E} \...
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Looking for a mathematical model that explains the increase of heat intensity while time is going on [closed]

Consider we are overloading a CPI device with many tasks. It is obvious that the CPU temperature goes up when the time is increasing. Is there anyone who can help with modeling this phenomenon?
1 vote
2 answers
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When $C_v=\partial E/ \partial T$?

$C_v=(\delta Q/dT)_v$, but sometime $C_v= \partial E/ \partial T$. If $\delta W=-PdV$ than it’s easy because $(\delta Q)_v=dE$. But for paramagnetic materials even if $\delta W=-PdV+BdM$ we have $C_v=\...
1 vote
1 answer
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Third law of thermodynamics conundrum with cyclic machines

Consider 3 objects, each with different heat capacities ($C_1$, $C_2$, $C_3$) and initial temperatures $T_1$, $T_2$, and $T_3$. Heat engines (HE1 and HE2) are placed between the objects to generate ...
0 votes
1 answer
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What's the amount of heat flowing to this system? [closed]

Im stuck trying to understand the solution to this question. Q: A thermodynamic system is defined by the equations - $P^2V = aNK_bT$, where $a>0$ and N>0 are constants. what is the amount of ...
5 votes
9 answers
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Can heat(?) flow from a cold object to hot object?

When we dip a spoon (stainless steel) into ice cream, does it becomes cold or stay the same temperature? If it does, can we say that heat(?) can flow from cold to hot objects? Is this the reason ...
4 votes
2 answers
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Entropy increase while in equilibrium paradox

Suppose that we have two containers containing an ideal gas and both have energy $E_1 = E_2 = E$, $V_1 = V_2 = V$ and $n_1 = n_2 = n$ which implies that they also have the same temperature (assuming ...
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2 answers
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Boltzmann distribution and probability of finding the system with specific energy

For sake of simplicity assume classical discrete systems. If we have a system ($\text{S}$) coupled to a reservoir ($\text{R}$), then a microstate of the combined (isolated with fixed energy $E$) ...
5 votes
7 answers
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Why do dark objects absorb visible light but only emit infrared radiation?

What is it about the molecular structure of dark coloured objects that means they absorb most of the visible light that falls on them, but radiate infrared? Naively I would think that if a molecule ...
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1 answer
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Can the Efficiency of an Arbitrary Reversible Cycle be Equal to the Efficiency of the Enclosing Carnot Cycle?

I was reading the following article: https://www.researchgate.net/publication/...
11 votes
3 answers
873 views

How do you measure the chemical potential?

It is clear how to measure thermodynamics quantities such as temperature, pressure, energy, particle number and volume. But I have no idea how to measure chemical potential. Could someone please ...
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1 answer
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In real life, can entropy decreases bring the dead back to life, make the old ones young, or make the born ones unborn, like in the movie Tenet? [closed]

In real life, can entropy reduction bring the dead back to life, make the old ones young, or make the born ones unborn, like in the movie Tenet? Is that likely? Does the existence of a probability of ...
3 votes
1 answer
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Postulates of statistical mechanics

Do we have postulates of statistical mechanics the way we have for quantum mechanics?
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5 answers
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Why aren't fusion reactors using centrifuges?

If fusing of nuclei in stars requires pressure, heat, and gravity, why not use a centrifuge to increase the gravity? We currently have the technology to make diamonds, and generate immense ...
0 votes
1 answer
150 views

How does a microwave steamer work?

While I am no physicist, I am convinced this is a physics question: How does a microwave steamer work? It seems like a scam to me. Wouldn't the microwave be cooking the food and heating the water at ...
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1 answer
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How was the black body intensity vs wavelength (or frequency) radiation curve historically produced?

I have read that Wilhelm Wien gave his formula to match the radiation curve of a black body as shown in the picture; which works well in high frequency region. Another formula by Rayleigh-Jeans is ...
2 votes
1 answer
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What is the most intense wavelength and frequency in the spectrum of a black body? [duplicate]

Planck's Law is commonly stated in two different ways: $$ u_\lambda \left( \lambda, T \right) = \frac{2hc^2}{\lambda^5} \frac{1}{e^\frac{hc}{\lambda kT}-1} $$ $$ u_\nu \left( \nu, T \right) = \frac{2h\...
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1 answer
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When are Dufour and Soret effects non-negligible?

Dufour effect is often times excluded from energy equations without mentioning. But there are many papers (out of my iq-league) which study effects of these phenomena in chemically reacting flows. ...
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1 answer
267 views

Fan and venturi effect

A simple calculation shows the power $P$ you can get from wind at speed $v$ passing through an area $A$ is (in Watts) $$P = 1.23\,v^3 \frac{A}{2}.$$ Using the above equation and taking the Venturi ...
1 vote
1 answer
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Using Helmholtz Free Energy to Calculate Liquid Density

My objective is to find an equation of state (EoS) for density, i.e. density as a function of pressure, temperature and concentration, for aqueous acids, bases and salts. A StackExchange user ...
0 votes
1 answer
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What is the temperature of vacuum?

I wonder what the temperature of vacuum is. Is it the absolute zero? The vacuum is defined without taking into account the Unruh effect or the CMB,it is just vacuum with nothing in it but quantum ...
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2 answers
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What is the entropy associated with a diffusion process?

Is it possible to calculate entropy from the solution of a diffusion equation(with natural boundary conditions) by using the formula of Shanon entropy? Could anyone help me to understand the entropic ...
19 votes
6 answers
8k views

How can I understand a Vortex Tube and its efficiency?

A Vortex Tube takes a pressurized input stream, most typically of a gas, and creates two output streams with a temperature differential. Apparently, it has been described as a Maxwell's Demon. Both ...
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1 answer
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Do liquids in tall containers or wide containers cool faster?

Given two containers of equal volume, one tall and thin, one short and wide, containing the same liquid at the same temperature, pressure, etc... which one would cool faster?
1 vote
2 answers
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Statics and dynamics in elasticity : how to add time in elasticity

In elasticity, there is are static relations of the form $R(\sigma,\epsilon)=0$. In fluid dynamics, there is a dynamics relation with the conservation of momentum leading to Navier-Stokes equation. ...
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0 answers
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If our planet had more gravitational force would rain clouds still form? [closed]

If the air pressure on Earth at sea level were 25 psi (about 172.000 Pascals), would rain clouds still form?
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1 answer
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Entropy vs dimension of the Hilbert space

In the definition of thermodynamic entropy $S=k\ln\Omega$ where $\Omega$ is the number of possible microstates of a given macrostate, we can also associate $\Omega$ with the dimension of the Hilbert ...
8 votes
1 answer
759 views

Why does symmetry reduce heat capacity?

For monatomic gasses, the heat capacity approaches $3R/2$ because there are three degrees of freedom (DOF) of translational motion. For diatomic gasses it approaches $7R/2$ because the symmetry about ...
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2 answers
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Water in house to heat and cool? [closed]

In the summer, when it reaches 27c during the day I want it to be colder, and when it reaches 15c at night I want it to be warmer. Is it possible to do some of this heating and cooling with water (...
0 votes
1 answer
200 views

How do you Find the Variance of Temperature in a Maxwell Boltzmann Distribution?

In Understanding Molecular Simulation, the following Maxwell Boltzmann distribution for momentum is given: $$\mathcal{P}(p) = \left(\frac{\beta}{2\pi m}\right)^{3/2}\text{exp}\left[\frac{-\beta p^2}{...
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When the temperature increases to four times the starting temperature, how are the equations for $\overline Z$ and $\overline \lambda$ affected? [closed]

A certain amount of ideal gas is stored in a container of fixed volume, the initial temperature is $T_0$, the average velocity $\overline v_0$, and the average collision frequency $\overline Z_0$. If ...
-2 votes
2 answers
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Can anyone prove this overstated-but-almost-never-justified fact from thermodynamics?

Clausius inequality states that $\oint {\delta Q\over T}$ equals zero for a system undergoing a reversible cycle, whereas it can’t be greater than zero for an irreversible cycle. But everywhere, I ...
11 votes
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Why can't we define more Maxwell's relations?

Let us define a new thermodynamic function $X$ such that, $$dX = TdS + PdV$$ where $T$ is the temperature of the system, $S$ is the entropy, $P$ is the pressure and $V$ is the volume. Now since $X$ ...
3 votes
2 answers
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Proof for $\oint \frac{dQ}{T}=0 $ in a reversible process

I'm actually trying to prove that Entropy is a state function. I get struck at the point where I need to prove that $\oint \frac{dQ}{T}=0 $ for a reversible process. Clausius in his book The ...
3 votes
2 answers
473 views

Is diffusion a nonequlibrium process?

We know that the diffusion equation can be viewed as the continuum limit of a discreet unbiased random walk. My question is the following: Is diffusion (or an unbiased random walk) a non-equilibrium ...
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0 answers
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Thermodynamics entropy physics [closed]

At 1C temperature, for ice to change in liquid the change in entropy for system is less negative, then the change in entropy for sorrounding which is more positive, so why is that? Although the bond ...
0 votes
1 answer
171 views

Thermal diffusion equation with heat per unit length?

Let us say we have a metal rod. Along that rod there is a rate of heat generation of H per unit length. If we assume we are in the steady state then I would expect us (from the thermal diffusion ...
7 votes
3 answers
362 views

How statistical thermodynamics actually solves these problems?

Our primary objective in thermodynamics is to explain the bulk behavior of matter. In trying to do so we may think of going with the straightforward approach of explaining the bulk behavior by ...
10 votes
5 answers
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Adiabatic piston: why is Callen's argument flawed?

This question is related to this one. I would ask you to read that question and my answer to the question itself before answering this one. The problem is the following. In his book Thermodynamics, ...
3 votes
1 answer
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Strange units of measurement of heat transfer coefficient in Newton's cooling law

In my finite element software there is the following equation: in the original Newton's cooling law h has the units $W/(m^2 K)$. Why here it has the units $W/(m^3 K)$? Thank you so much.
2 votes
1 answer
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What is the mean free path (MFP) of a Cosmic microwave background radiation (CMBR) photon?

If the IGM (inter-galactic medium) had a massive particle (proton) every cubic metre, or a carbon grain every cubic kilometre, what would be the MFP of a CMBR photon? The coherence length of the ...
2 votes
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Maxwell distribution solely using the Stosszahlansatz and geometric transformations?

Background To quote Wikipedia: The assumption of molecular chaos is the key ingredient that allows proceeding from the BBGKY hierarchy to Boltzmann's equation, by reducing the 2-particle distribution ...
2 votes
2 answers
374 views

Include other degrees of freedom in Maxwell-Boltzmann Distribution possible?

According to Boltzmann statistics the number of particles $n$ with a certain energy level $E_j$ in case of discrete energy levels is: $$n(E_j) = \frac{N}{Z} \cdot e^{-\frac{E_j}{k_B T}} \cdot g_j$$ ...
1 vote
2 answers
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Predicting the effect of a power outage on the temperature in my fridge

I have a commercial fridge, without a freezer. It is vertical fridge with one glass door. We have medications we want to keep below 8°C. Most medication tolerate a slight T elevation without problem. ...
6 votes
3 answers
2k views

Why are thermodynamic potentials minimised?

Why is it that, at equilibrium, certain potentials are minimised? That is, for a system at constant temperature and pressure, the Gibbs free energy is minimised, and for fixed volume and temperature, ...
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1 answer
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Is it possible to define concepts like free energy in the diffusion process?

How does the idea of free energy (which we derive from the canonical partition function) fit in the domain of non-equilibrium processes like diffusion?
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2 answers
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Legendre transformation: non-convex/non-convave functions

The Legendre transformation is used to derive the Hamiltonian from the Lagrangian, and it finds many applications in thermodynamics to convert between the different potentials. $ f(x) \rightarrow g(u)...
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1 answer
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I'm confused when to use Bernoulli's equation and continuity momentum equation

Conflicts between Bernoulli's Equation and Momentum Conservation? 1). Is this equation compatible with any case? And how? 2). Isn't $\rho u$ from the derivation of the Bernoulli's equation a ...
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How can I safely heat up a AAA battery? [duplicate]

I’m working on a science experiment in whether or not the temperature of a battery affects how long it will last. It’s the middle of winter where I am and I’m not quite sure how to safely heat up the ...
1 vote
1 answer
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An isolated Earth

It is known the fact that there is no way to extract energy (in any form) from any system without introducing some energy. The Earth for example, gets energy from the Sun, from nuclear fusion of ...

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